where \(a\in \mathbb {C}\setminus \lbrace 0,1\rbrace \) ,
and the points \(x=0,1,a,\infty \)  are regular singularities.
If \(a=0\)  and \(a=1\)  the above equation
can be reduced to the Gauss hypergeometric equation [1]}
\(\begin{array}{l}z(1-z)\frac{d^{2}Z(z)}{dz^{2}}+\big [\mathrm {c}-(\mathrm {a}+\mathrm {b}+1)z\big ]\frac{dZ(z)}{dz}-\mathrm {a}\mathrm {b}\;Z(z)=0,\end{array}\) 
